Our global approach complements modular, bottom-up constructions [1]}, like process theories based on symmetric monoidal categories [2]}, [3]}, [4]}, [5]}, [6]}.
For the purpose of comparison with our work, modular theories can be understood as theories of individual systems (or “objects”) and local actions (“processes”) on those systems, which allow for parallel and sequential composition of processes on different systems. Typically, they assume that:
1)
Processes with matching output and input systems can be composed sequentially. That is, a process \(f: A \rightarrow A^{\prime }\)  can be composed with a process \(g: A^{\prime } \rightarrow A^{\prime \prime }\) , to form a new process \(g \circ f: A \rightarrow A^{\prime \prime }\)  satisfying
\( g \circ f (A) = g ( f(A)) \) 
